Our E-300 will not power up. Absolutely nothing happens when it is turned on.
Initially we thought the battery was not holding charge so we purchased a new
one. But even with the new, fully charged battery, nothing happens.
The camera has a standard 14-45mm lens and has no memory card inserted.
It is approx. 15 months old with no previous problems.
Any ideas?

Besides looking to see that the electrical contacts in the battery compartment look OK, and that the mode dial is not between two modes (it's locked on the mode), it's time for the camera to take a trip to Olympus or Olympus authorized repair depot.